"In that case it's a windward/leeward encounter where the windward boat must keep clear, putting the onus on the running vessel to avoid the other. "
I looked in the latest rules and saw windward/leeward rules for boats overtaking, mast abeam, all sorts of things but nothing that seemed to apply to boats closing from opposite directions.
Which Rule covers this?

This thread has very explicit answers to your question. If they're on the same tack, the windward boat must keep clear. If they're on opposite tacks, the Port Tack boat must keep clear. In either case, the crossing is likely to be quick, with one boat headed upwind and the other down. If your rule book contains "Mast abeam", you need a new one. "Mast abeam" was deleted from the rules at least two versions - about eight years ago. Anyone calling out "mast abeam" in a race today is either purposely joking or telling me he has no idea whatsoever about the rules. For the most up-to-date version, go to the source: http://www.ussailing.org/rules/